Problem: $86$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $31$ less than $2$ times the number of away team fans. How many home team and away team fans attended the game?
Solution: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 86}$ ${x = 2y-31}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${2y-31}$ for $x$ in the first equation. ${(2y-31)}{+ y = 86}$ Simplify and solve for $y$ $ 2y-31 + y = 86 $ $ 3y-31 = 86 $ $ 3y = 117 $ $ y = \dfrac{117}{3} $ ${y = 39}$ Now that you know ${y = 39}$ , plug it back into ${x = 2y-31}$ to find $x$ ${x = 2}{(39)}{ - 31}$ $x = 78 - 31$ ${x = 47}$ You can also plug ${y = 39}$ into ${x+y = 86}$ and get the same answer for $x$ ${x + }{(39)}{= 86}$ ${x = 47}$ There were $47$ home team fans and $39$ away team fans.